Paris, confident of its charms (overconfident, as it turned out about the 2012 Olympic Games), doesn't usually bother with a summer festival once its citizens leave on holiday.

But this July, it has inaugurated an out-of-doors spectacle, Les Étés de la Danse de Paris, to rival festivals in southern cities such as Avignon, Aix and Montpellier. Valéry Colin, a former dancer with the Paris Opera Ballet, has convinced the capital's authorities, and sponsors, that locals and tourists will benefit from al fresco dance performances on balmy evenings.

He and his advisers chose San Francisco Ballet as the first invited company because of its varied repertoire and much-admired standards of dancing. (SFB is one of Britain's favourite foreign visitors.) Brushing aside any French anti-Americanism, Colin asked the company to open with all-American works made specially for the occasion.

The catch, of course, is that Paris's weather is as unreliable as London's. On Tuesday's opening night, thunder clouds loomed and 2,000 spectators shivered on bleachers in the courtyard of the 18th-century palaces housing the National Archives. The setting was, none the less, magnificent, as wind shook the coppiced planes around the rose garden and blew the draperies of dancers on the (covered) stage. Behind them was the neoclassical facade of the Hotel de Rohan, lending an air of formality to their New World exuberance.

Madame Chirac was present, the President having left for the G8 summit. The only protest came in leaflets handed out by employees of the National Archives, indignant that money was being lavished on dance instead of jobs and better conditions. The dancers, who could have refused to perform in chilly conditions, carried on blithely.

The programme started with two formulaic works by veteran choreographers: Paul Taylor's Spring Rounds and Lar Lubovitch's Elemental Brubeck. Taylor can do vernal like nobody else, but he's done it many times before. Fourteen dancers in lime green waltz and frolic affably to Richard Strauss, the women swept into the men's arms like children at play.

Lubovitch updates the social dancing to Broadway-style jazz, set to Brubeck pieces from the 1960s. A showoff in red, Gonzalo Garcia never quite integrates with the rest of the gang; maybe they're fantasy companions, leaving him predictably alone at the end. Moods range from bluesy to ballsy, in dance styles from bebop to Bob Fosse showbiz. Though the boys and girls get a warm workout, the exercise merely reinforces stereotypes of American popular dance.

And then comes Christopher Wheeldon's new piece, his fourth for this company, and the concluding jewel of the evening. Like others, SFB regards him as the white hope of ballet. For Quaternary, he has juxtaposed scores that inspire him, taking the four seasons as a linking pretext. The structure just about holds. Lit by Jennifer Tipton, the four-part ballet looks classical and contemporary, perfect for its Parisian setting.

'Winter' (to John Cage) has Yuan Yuan Tan as an elegant frost fairy, scudding on point as if across an icy surface. 'Spring' (to Bach) combines two couples in a cascade of steps, echoing Taylor's carefree waltzes. Pellucid piano (Arvo Pärt) accompanies a hazy 'Summer' duet for Muriel Maffre and Yuri Possokhov: weirdly ethereal, she seems conjured up by her partner's delirium. 'Autumn' (to Steven Mackey's electric guitar) whirls an ensemble that displays buoyant American ballet at its best. The audience stamp their frozen feet in acclamation.